What should be added to the polynomial x² – 5x + 4, so that 3 is the zero of the resulting polynomial?

Given;

p(x) = x² – 5x + 4

3 is the zero of the resulting polynomial

So we have;

p(3) = (3)² – 5×3 + 4

p(3) = 9 – 15 + 4

p(3) = – 2

As – 2 is the remainder,

So 2 should be added to the given polynomial to get 3 as the zero of the resulting polynomial.

We can also verify the answer;

By adding 2 to the given polynomial we get;

P(x) = x² – 5x + 4 + 2

P(x) = x² – 5x + 6

P(3) = 9 – 15 + 6

P(3) = 15 – 15

P(3) = 0

Hence prooved that 2 is the right answer to get 3 as the zero of resulting polynomial.